Statistics and Data Analysis for Microarrays Using R and Bioconductor, 2nd Edition

Analysis and visualization tools 553

two axes, the clusters corresponding to the two c lasses overlap and the classes

cannot be separated using any single dimension. Therefo re, a dimensionality

reduction is not possible in the original coordinate system. In order to separate

the two classes, one needs both x

1

and x

2

. However, the PCA approach can

analyze the data and extract from it a new coordinate system with axes p

1

and p

2

. The direction of the new axes will be the direction in which the data

have the largest and second largest variance. If the two clusters are projected

on the axes of the new coordinate sys tems one can notice that the situation

is now different. The projections of the two classes on p

2

overlap completely.

However, the projections ...